Properties

Label 43200.gt
Number of curves $3$
Conductor $43200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gt1")
 
E.isogeny_class()
 

Elliptic curves in class 43200.gt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43200.gt1 43200dc3 \([0, 0, 0, -197100, -44658000]\) \(-1167051/512\) \(-371504185344000000\) \([]\) \(373248\) \(2.0785\)  
43200.gt2 43200dc1 \([0, 0, 0, -5100, 142000]\) \(-132651/2\) \(-221184000000\) \([]\) \(41472\) \(0.97993\) \(\Gamma_0(N)\)-optimal
43200.gt3 43200dc2 \([0, 0, 0, 18900, 702000]\) \(9261/8\) \(-644972544000000\) \([]\) \(124416\) \(1.5292\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43200.gt have rank \(0\).

Complex multiplication

The elliptic curves in class 43200.gt do not have complex multiplication.

Modular form 43200.2.a.gt

sage: E.q_eigenform(10)
 
\(q + q^{7} + 3 q^{11} - 4 q^{13} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.